Wind Effects on Cable-Supported Bridges

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  • Format: Hardcover
  • Copyright: 2013-04-09
  • Publisher: Wiley

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An in-depth guide to understanding wind effects on cable supported bridges, this book uses analytical, numerical and experimental methods to give readers a practical understanding. It is structured to systemically move from introductory areas through to advanced topics currently being developed from research work. The book concludes with the application of the theory covered to real-world examples, enabling readers to apply their knowledge. The author provides background material on the topic first of all, covering areas such as wind climate, cable-supported bridges, wind-induced damage, and the history of bridge wind engineering. Wind characteristics in atmospheric boundary layer, mean wind load and aerostatic instability, wind-induced vibration and aerodynamic instability, and wind tunnel testing are then described as the fundamentals of the subject. State-of-the-art contributions include wind and rain-induced cable vibration, wind-vehicle-bridge interactions, wind-induced vibration control, wind and structural health monitoring, and probabilistic evaluation and reliability analysis. Finally the theory is applied to the Tsing Ma suspension bridge and the Stonecutters cable-stayed bridge in Hong Kong. Amongst the world's longest bridges, both are located in one of the world's most active typhoon regions and equipped with incredibly comprehensive structural health monitoring systems. The book will therefore bridge the gap between the theoretical research and practical applications.

Author Biography

You Lin Xu, The Hong Kong Polytechnic University, China
Prof. Y L Xu obtained his Doctorate from The University of Sydney, Australia, in 1991. Having worked at James Cook University, Australia, as a research fellow from 1991-95, he joined The Hong Kong Polytechnic University in 1995. He was promoted to Professor in 1999 and to Chair Professor in 2003. Prof. Xu has been the founding Director of Research Centre for Urban Hazards Mitigation of the University since 2002, and was appointed as Head of the Department of Civil and Structural Engineering of the University in 2007.
Prof. Xu has conducted research and consultancy work in the field of wind engineering and bridge engineering for almost 30 years. He has worked extensively on wind loading and effect on the Tsing Ma suspension bridge in Hong Kong since 1995. Prof. Xu has also been heavily involved in wind studies of the Stonecutters Bridge in Hong Kong. At The Hong Kong Polytechnic University, Prof. Xu has taught the subject "Wind Engineering" to MSc students since 1998. He has edited 5 books, published over 160 refereed international journal papers, and presented over 200 conference papers. Prof. Xu is a Fellow Member of the Hong Kong Institution of Engineers (HKIE) and a Fellow Member of the American Society of Civil Engineer (ASCE).

Table of Contents




1 Wind Storms and Cable-Supported Bridges

1.1 Preview

1.2 Basic Notions of Meteorology

1.2.1 Global wind circulations

1.2.2 Pressure gradient force

1.2.3 Coriolis force

1.2.4 Geostrophic wind

1.2.5 Gradient wind

1.2.6 Frictional effects     

1.3 Basic Types of Wind Storms

1.3.1 Gales from large depressions

1.3.2 Monsoons
1.3.3 Tropical cyclones (hurricanes or typhoons)

1.3.4 Thunderstorms

1.3.5 Downbursts

1.3.6 Tornadoes

1.3.7 Downslope winds

1.4 Basic Types of Cable-Supported Bridges

1.4.1 Main features of cable-supported bridges

1.4.2 Suspension bridges

1.4.3 Cable-stayed bridges

1.4.4 Hybrid cable-supported bridges

1.5 Wind Damage to Cable-Supported Bridges

1.5.1 Suspension bridges

1.5.2 Cable-stayed bridges

1.5.3 Stay cables

1.5.4 Road vehicles running on bridge

1.6 History of Bridge Aerodynamics

1.7 Organization of the Book

1.8 References

1.9 Notations

2 Wind Characteristics in Atmospheric Boundary Layer

2.1 Preview

2.2 Turbulent Winds in Atmospheric Boundary Layer

2.3 Mean Wind Speed Profiles

2.3.1 The “Logarithmic law”

2.3.2 The “Power law”

2.3.3 Mean wind speed profile over ocean

2.3.4 Mean wind speed profile in tropical cyclone

2.4 Wind Turbulence

2.4.1 Standard deviations

2.4.2 Turbulence intensities

2.4.3 Time scales and integral length scales

2.4.4 Probability density functions
2.4.5 Power spectral density functions

2.4.6 Covariance and correlation

2.4.7 Cross-spectrum and coherence

2.4.8 Gust wind speed and gust factor

2.5 Terrain and Topographic Effects
2.5.1 Change of surface roughness

2.5.2 Amplification of wind by hills

2.5.3 Amplification factor and speed-up ratio

2.5.4 Funneling effect

2.6 Design Wind Speeds

2.6.1 Exceedance probability and return period

2.6.2 Probability distribution function

2.6.3 Generalized extreme value distribution

2.6.4 Extreme wind estimation by the Gumbel distribution

2.6.5 Extreme wind estimation by the method of moments

2.6.6 Design life span and risk

2.6.7 Parent wind distribution

2.7 Directional Preference of High Winds

2.8 Case Study: Tsing Ma Bridge Site

2.8.1 Anemometers in WASHMS

2.8.2 Typhoon wind characteristics

2.8.3 Monsoon wind and joint probability density function

2.9 References

2.10 Notations

3 Mean Wind Load and Aerostatic Instability

3.1 Preview   

3.2 Mean Wind Load and Force Coefficients

3.2.1 Bernoulli’s equation and wind pressure

3.2.2 Mean wind load

3.2.3 Wind force coefficients

3.3 Torsional Divergence

3.4 3D Aerostatic Instability Analysis

3.5 Finite Element Modeling of Long-Span Cable-Supported Bridges

3.5.1 Theoretical background

3.5.2 Spine beam model

3.5.3 Multi-scale model

3.5.4 Modeling of cables

3.6 Mean Wind Response Analysis

3.6.1 Determination of reference position

3.6.2 Mean wind response analysis

3.7 Case Study: Stonecutters Bridge 

3.7.1 Main features of Stonecutters Bridge

3.7.2 Finite element modeling of Stonecutters Bridge

3.7.3 Aerodynamic coefficients of bridge components

3.7.4 Mean wind response analysis

3.8 References

3.9 Notations

4 Wind-Induced Vibration and Aerodynamic Instability

4.1 Preview

4.2 Vortex-Induced Vibration

4.2.1 Reynolds number and vortex shedding

4.2.2 Strouhal number and lock-in

4.2.3 Vortex-induced vibration

4.3 Galloping Instability

4.3.1 Galloping mechanism

4.3.2 Criterion for galloping instability

4.3.3 Wake galloping

4.4 Flutter Analysis

4.4.1 Introduction 

4.4.2 Self-excited forces and aerodynamic derivatives

4.4.3 Theodorsen circulatory function

4.4.4 1D flutter analysis

4.4.5 2D flutter analysis

4.4.6 3D flutter analysis in frequency domain

4.4.7 Flutter analysis in time domain

4.5 Buffeting Analysis in Frequency Domain

4.5.1 Background

4.5.2 Buffeting forces and aerodynamic admittances

4.5.3 3D buffeting analysis in frequency domain

4.6 Simulation of Stationary Wind Field

4.7 Buffeting Analysis in Time Domain

4.8 Effective Static Loading Distributions

4.8.1 Gust response factor and peak factor

4.8.2 Effective static loading distributions

4.9 Case Study: Stonecutters Bridge

4.9.1 Dynamic and aerodynamic characteristics of Stonecutters Bridge

4.9.2 Flutter analysis of Stonecutters Bridge

4.9.3 Buffeting analysis of Stonecutters Bridge

4.10 References

4.11 Notations

5 Wind-Induced Vibration of Stay Cables

5.1 Preview

5.2 Fundamentals of Cable Dynamics
5.2.1 Vibration of a taut string

5.2.2 Vibration of an inclined cable with sag

5.3 Wind-Induced Cable Vibrations

5.3.1 Buffeting by wind turbulence

5.3.2 Vortex-induced vibration

5.3.3 Galloping of dry inclined cables

5.3.4 Wake galloping for groups of cables

5.4 Mechanism of Rain-Wind-Induced Cable Vibration

5.4.1 Background

5.4.2 Analytical model of SDOF

5.4.3 Horizontal cylinder with fixed rivulet

5.4.4 Inclined cylinder with moving rivulet

5.4.5 Analytical model of 2DOF

5.5 Prediction of Rain-Wind-Induced Cable Vibration

5.5.1 Analytical model for full scale stay cables

5.5.2 Prediction of rain wind induced vibration of full scale stay cable

5.5.3 Parameter studies

5.6 Occurrence Probability of Rain-Wind-Induced Cable Vibration

5.6.1 Joint probability density function (JPDF) of wind speed and direction

5.6.2 Probability density function of rainfall intensity

5.6.3 Occurrence range of rain-wind-induced cable vibration

5.6.4 Occurrence probability of rain-wind-induced cable vibration

5.7 Case Study: Stonecutters Bridge

5.7.1 Statistical analysis of wind data
5.7.2 Joint probability density function of wind speed and wind direction

5.7.3 Statistical analysis of rainfall data

5.7.4 Probability density function of rainfall intensity

5.7.5 Occurrence range of rain-wind-induced cable vibration

5.7.6 Hourly occurrence probability and annual risk

5.8 References

5.9 Notations

6 Wind-Vehicle-Bridge Interaction

6.1 Preview   

6.2 Wind-Road Vehicle Interaction

6.2.1 Wind-induced vehicle accidents

6.2.2 Modeling of road vehicle

6.2.3 Modeling of road surface roughness

6.2.4 Aerodynamic forces and moments on road vehicle

6.2.5 Governing equations of motion of road vehicle

6.2.6 Case study

6.2.7 Effects of road surface roughness

6.2.8 Effects of vehicle suspension system

6.2.9 Accident vehicle speed

6.3 Formulation of Wind-Road Vehicle-Bridge Interaction

6.3.1 Equations of motion of coupled road vehicle-bridge system

6.3.2 Equations of motion of coupled wind-road vehicle-bridge system

6.4 Safety Analysis of Road Vehicles on Ting Kau Bridge under Crosswind

6.4.1 Ting Kau Bridge

6.4.2 Wind forces on bridge

6.4.3 Scenario for extreme case study

6.4.4 Dynamic response of high sided road vehicle

6.4.5 Accident vehicle speed

6.4.6 Comparison of safety of road vehicle running on bridge and ground

6.5 Formulation of Wind-Railway Vehicle Interaction

6.5.1 Modelling of vehicle subsystem

6.5.2 Modelling of track subsystem

6.5.3 Wheel and rail interaction

6.5.4 Rail irregularity

6.5.5 Wind forces on ground railway vehicles
6.5.6 Numerical solution

6.6 Safety and Ride Comfort of Ground Railway Vehicle under Crosswind

6.6.1 Vehicle and track models

6.6.2 Wind forces on railway vehicle

6.6.3 Rail irregularity

6.6.4 Response of coupled vehicle-track system in crosswind

6.6.5 Safety and ride comfort performance

6.7Wind-Railway Vehicle-Bridge Interaction: Tsing Ma Bridge

6.7.1 Formulation of wind-railway vehicle-bridge interaction

6.7.2 Engineering approach for determining wind forces on moving vehicle

6.7.3 Case study

6.8 References

6.9 Notations

7 Wind Tunnel Studies

7.1 Preview

7.2 Boundary Layer Wind Tunnels

7.2.1 Open-circuit wind tunnel

7.2.2 Closed-circuit wind tunnel

7.2.3 Actively controlled wind tunnel

7.3 Model Scaling Requirements

7.3.1 General model scaling requirements

7.3.2 Notes on model scaling requirements

7.3.3 Blockage consideration

7.4 Boundary Wind Simulation

7.4.1 Natural growth method

7.4.2 Augmented method

7.4.3 Actively-controlled grids and spires

7.4.4 Actively-controlled multiple fans

7.4.5 Topographic models

7.4.6 Instrumentation for wind measurement in wind tunnel

7.5 Sectional Model Tests

7.5.1 Models and scaling

7.5.2 Section model tests for force coefficients

7.5.3 Section model tests for flutter derivatives and vortex-induced vibration

7.5.4 Section model tests with pressure measurements

7.5.5 Section model tests for aerodynamic admittance

7.6 Taut Strip Model Tests

7.7 Full Aeroelastic Model Tests

7.8 Identification of Flutter Derivatives

7.8.1 Free vibration test of section model

7.8.2 Forced vibration test of section model

7.8.3 Free vibration test of taut strip model and full aeroelastic model

7.9 Identification of Aerodynamic Admittance 

7.10 Cable Model Tests

7.10.1 Inclined dry cable tests

7.10.2 Rain-wind simulation of inclined stay cable

7.11 Vehicle-Bridge Model Tests

7.11.1 Vehicles on ground

7.11.2 Stationary vehicle on bridge deck

7.11.3 Moving vehicle on bridge deck

7.12 References

7.13 Notations

8 Computational Wind Engineering

8.1 Preview

8.2 Governing Equations of Fluid flow

8.2.1 Mass conservation

8.2.2 Momentum conservation

8.2.3 Energy conservation and Newtonian flow

8.2.4 Navier-Stokes equations

8.2.5 Governing equations of wind flow

8.3 Turbulence and its Modeling

8.3.1 Direct numerical simulation

8.3.2 Reynolds averaged method

8.3.3 Large eddy simulation

8.3.4 Detached eddy simulation

8.3.5 Discrete vortex method

8.4 Numerical Considerations

8.4.1 Finite difference method

8.4.2 Finite element method

8.4.3 Finite volume method

8.4.4 Solution algorithms for pressure-velocity coupling in steady flows

8.4.5 Solution for unsteady flows

8.4.6 Boundary conditions

8.4.7 Grid generation

8.4.8 Computing techniques

8.4.9 Verification and validation

8.4.10 Applications in bridge wind engineering

8.5 CFD for Force Coefficients of Bridge Deck

8.5.1 Computational domain

8.5.2 Meshing

8.5.3 Boundary conditions and numerical method

8.5.4 Aerodynamic force coefficients and flow field

8.6 CFD for Vehicle Aerodynamics

8.6.1 Computational domain

8.6.2 Meshing

8.6.3 Boundary conditions and numerical method

8.6.4 Simulation results

8.6.5 Vehicle moving on ground

8.7 CFD for Aerodynamics of Coupled Vehicle-Bridge Deck System

8.7.1 Computational domain

8.7.2 Meshing

8.7.3 Boundary conditions and numerical method

8.7.4 Simulation results

8.7.5 Moving vehicle on bridge deck

8.8 CFD for Flutter Derivatives of Bridge Deck

8.8.1 Modelling and meshing

8.8.2 Numerical method

8.8.3 Simulation results

8.9 CFD for Nonlinear Aerodynamic Forces on Bridge Deck

8.9.1 Modelling and meshing

8.9.2 Numerical method

8.9.3 Simulation results

8.10 References

8.11 Notations

9 Wind and Structural Health Monitoring

9.1 Preview

9.2 Design of Wind and Structural Health Monitoring Systems

9.3 Sensors and Sensing Technology

9.3.1 Anemometers and other wind measurement sensors

9.3.2 Accelerometers

9.3.3 Displacement transducers and level sensors

9.3.4 Global positioning systems

9.3.5 Strain gauges

9.3.6 Fiber optic sensors

9.3.7 Laser doppler vibrometers

9.3.8 Weather stations

9.3.9 Wireless sensors

9.4Data Acquisition and Transmission System

9.4.1 Configuration of DATS

9.4.2 Hardware of data acquisition units

9.4.3 Network and communication

9.4.4 Operation of Data Acquisition and Transmission

9.5 Data Processing and Control System

9.5.1 Data acquisition control

9.5.2 Signal pre-processing and post-processing

9.6 Data Management System

9.6.1 Components and functions of data management system

9.6.2 Maintenance of data management system

9.7 Structural Health Monitoring System of Tsing Ma Bridge

9.7.1 Overview of WASHMS

9.7.2 Anemometers in WASHMS

9.7.3 Temperature sensors in WASHMS

9.7.4 Displacement transducers in WASHMS

9.7.5 Level sensing stations in WASHMS

9.7.6 GPS in WASHMS

9.7.7 Strain gauges in WASHMS

9.7.8 Accelerometers in WASHMS

9.8 Monitoring Results of Tsing Ma Bride during Typhoon Victor

9.8.1 Typhoon Victor

9.8.2 Local topography

9.8.3 Calculations of mean wind speed and fluctuating wind components

9.8.4 Mean wind speed and direction

9.8.5 Turbulence intensity and integral scale

9.8.6 Wind spectra

9.8.7 Acceleration response of bridge deck

9.8.8 Acceleration response of bridge cable

9.8.9 Remarks

9.9 System Identification of Tsing Ma Bridge during Typhoon Victor

9.9.1 Background

9.9.2 EMD+HT method

9.9.3 Natural frequencies and modal damping ratios

9.10 References

9.11 Notations

10 Buffeting Response to Skew Winds

10.1 Preview

10.2 Formulation in the Frequency Domain

10.2.1 Basic assumptions

10.2.2 Coordinate systems and transformation matrices

10.2.3 Wind components and directions

10.2.4 Buffeting forces and spectra under skew winds

10.2.5 Aeroelastic forces under skew winds

10.2.6 Governing equation and solution in the frequency domain

10.3 Formulation in the Time Domain

10.3.1 Buffeting forces due to skew winds in time domain

10.3.2 Self-excited forces due to skew winds in time domain

10.3.3 Governing equation and solution in the time domain

10.4 Aerodynamic Coefficients of Bridge Deck under Skew Winds

10.5 Flutter Derivatives of Bridge Deck under Skew Winds

10.6 Aerodynamic Coefficients of Bridge Tower under Skew Winds

10.7 Comparison with Field Measurement Results of Tsing Ma Bridge

10.7.1 Typhoon Sam and measured wind data

10.7.2 Measured bridge acceleration responses

10.7.3 Input data to computer simulation

10.7.4 Comparison of buffeting response in the frequency domain

10.7.5 Comparison of buffeting response in the time domain

10.8 References

10.9 Notations

11 Multiple Loading-Induced Fatigue Analysis

11.1 Preview

11.2 SHM-Oriented Finite Element Modeling

11.2.1 Background

11.2.2 Main features of Tsing Ma Bridge

11.2.3 Finite element modelling of Tsing Ma Bridge

11.3 Framework for Buffeting-Induced Stress Analysis

11.3.1 Equation of motion

11.3.2 Buffeting forces

11.3.3 Self-excited forces

11.3.4 Determination of bridge responses

11.4 Comparison with Field Measurement Results of Tsing Ma Bridge

11.4.1 Wind characteristics

11.4.2 Measured acceleration responses of bridge deck

11.4.3 Measured stresses of bridge deck

11.4.4 Wind field simulation

11.4.5 Buffeting forces and self excited forces

11.4.6 Comparison of bridge acceleration responses

11.4.7 Comparison of bridge stress responses

11.5 Buffeting-Induced Fatigue Damage Assessment

11.5.1 Background

11.5.2 Joint probability density function of wind speed and direction

11.5.3 Critical stresses and hot spot stresses

11.5.4 Hot spot stress characteristics

11.5.5 Damage evolution model

11.5.6 Buffeting induced fatigue damage assessment

11.6 Framework for Multiple Loading-induced Stress Analysis

11.6.1 Equation of motion

11.6.2 Pseudo forces in trains and road vehicles

11.6.3 Contact forces between train and bridge

11.6.4 Contact forces between road vehicles and bridge

11.6.5 Wind forces on bridge

11.6.6 Wind forces on vehicles

11.6.7 Numerical solution

11.7 Verification by Case Study: Tsing Ma Bridge

11.7.1 Finite element models of bridge, train and road vehicles

11.7.2 Rail irregularities and road roughness

11.7.3 Wind force simulation

11.7.4 Selected results

11.8 Fatigue Analysis of Long-Span Suspension Bridge under Multiple Loading

11.8.1 Establishment of framework

11.8.2 Simplifications used in engineering approach

11.8.3 Dynamic stress analysis using engineering approach

11.8.4 Verification of engineering approach

11.8.5. Determination of fatigue-critical locations

11.8.6 Databases of dynamic stress responses to different loadings

11.8.7 Multiple load-induced dynamic stress time histories in design life

11.8.8 Fatigue analysis at fatigue-critical locations

11.9 References

11.10 Notations

12 Wind-Induced Vibration Control

12.1 Preview

12.2 Control Methods for Wind-Induced Vibration

12.3 Aerodynamic Measures for Flutter Control

12.3.1 Passive aerodynamic measures

12.3.2 Active aerodynamic control

12.4 Aerodynamic Measures for Vortex-Induced Vibration Control

12.5 Aerodynamic Measures for Rain-Wind-Induced Cable Vibration Control

12.6 Mechanical Measures for Vortex-Induced Vibration Control

12.7 Mechanical Measures for Flutter Control

12.7.1 Passive control systems for flutter control

12.7.2 Active control systems for flutter control

12.7.3 Semi-active control systems for flutter control

12.8 Mechanical Measures for Buffeting Control

12.8.1 Multiple pressurized tuned liquid column dampers

12.8.2 Semi-active tuned liquid column dampers

12.9 Mechanical Measures for Rain-Wind-Induced Cable Vibration Control

12.10 Case Study:  Damping Stay Cables in a Cable-Stayed Bridge

12.11 References

12.12 Notations

13 Typhoon Wind Field Simulation

13.1 Preview

13.2 Refined Typhoon Wind Field Model

13.2.1 Background

13.2.2 Refined typhoon wind field model

13.2.3 Typhoon wind decay model

13.2.4 Remarks

13.3 Model Solutions

13.3.1 Decomposition method

13.3.2 Friction-free wind velocity

13.3.3 Friction-induced wind velocity

13.3.4 Procedure of typhoon wind field simulation

13.4 Model Validation

13.4.1 Typhoon York

13.4.2 Main parameters of Typhoon York

13.4.3 Wind field simulation at Waglan Island

13.4.4 Spatial distribution of typhoon wind field

13.4.5 Wind speed profiles in vertical direction

13.5 Monte Carlo Simulation

13.5.1 Background

13.5.2 Typhoon wind data

13.5.3 Probability distributions of key parameters

13.5.4 K-S test

13.5.5 Typhoon wind decay model parameters

13.5.6  Procedure for estimating extreme wind speeds and averaged wind speed profiles

13.6 Extreme Wind Analysis

13.6.1 Basic theory

13.6.2 Extreme wind speed analysis using the refined typhoon wind field model

13.6.3 Extreme wind speed analysis based on wind measurement data

13.6.4 Comparison of results and discussion

13.6.5 Mean wind speed profile analysis

13.7 Simulation of Typhoon Wind Field over Complex Terrain

13.7.1 Background

13.7.2 Directional upstream typhoon wind speeds and profiles

13.7.3 Representative directional typhoon wind speeds and profiles at site

13.7.4 Training ANN model for predicting directional typhoon wind speeds and profiles

13.7.5 Directional design typhoon wind speeds and profiles at site

13.8 Case Study: Stonecutters Bridge Site

13.8.1 Topographical conditions

13.8.2 Directional upstream typhoon wind speeds and profiles

13.8.3 Representative typhoon wind speeds and profiles

13.8.4 Establishment of ANN model

13.8.5 Directional design wind speeds and wind profiles

13.9 References

13.10 Notations

14 Reliability Analysis of Wind-Excited Bridges

14.1 Preview

14.2 Fundamentals of Reliability Analysis

14.2.1 Limit states

14.2.2 First-order second moment (FOSM) method

14.2.3 Hasofer and Lind (HL) method

14.2.4 Monte Carlo simulation (MCS) and response surface method (RSM)

14.2.5 Threshold crossing

14.2.6 Peak distribution

14.3 Reliability Analysis of Aerostatic Instability

14.4 Flutter Reliability Analysis

14.5 Buffeting Reliability Analysis

14.5.1 Failure model by first passage

14.5.2 Reliability analysis based on threshold crossings

14.5.3 Reliability analysis based on peak distribution

14.5.4 Notes on buffeting reliability analysis

14.6 Reliability Analysis of Vortex-Induced Vibration

14.7 Fatigue Reliability Analysis Based on Miner’s Rule for Tsing Ma Bridge

14.7.1 Framework for fatigue reliability analysis

14.7.2 Probabilistic model of railway loading

14.7.3 Probabilistic model of highway loading

14.7.4 Probabilistic model of wind loading

14.7.5 Multiple load-induced daily stochastic stress response

14.7.6 Probability distribution of the daily sum of M-power stress ranges

14.7.7 Probability distribution of the sum of M-power stress ranges within the period

14.7.8 Reliability analysis results

14.8 Fatigue Reliability Analysis Based on Continuum Damage Mechanics

14.8.1 Basic theory of continuum damage mechanics

14.8.2 Nonlinear properties of fatigue damage accumulation

14.8.3 Continuum damage model used in this study

14.8.4 Verification of continuum damage model

14.8.5 Framework of fatigue reliability analysis

14.8.6 Reliability analysis results

14.9 References

14.10 Notations

15 Non-Stationary and Nonlinear Buffeting Response

15.1 Preview

15.2 Non-Stationary Wind Model I

15.2.1 Non-stationary wind model I

15.2.2 Empirical mode decomposition

15.2.3 Non-stationary wind characteristics

15.2.4 Case study: Typhoon Victor

15.3 Non-Stationary Wind Model II

15.3.1 Time-varying mean wind speed and mean wind profile

15.3.2 Evolutionary spectra

15.3.3 Coherence function

15.3.4 Case study: Typhoon Dujuan 

15.4 Buffeting Response to Non-Stationary Wind

15.4.1 Time-varying mean wind forces

15.4.2 Non-stationary self-excited forces

15.4.3 Non-stationary buffeting forces

15.4.4 Governing equations of motion

15.4.5 Time-varying mean wind response

15.4.6 Modal equations for non-stationary buffeting response

15.4.7 Pseudo excitation method for solving modal equations

15.4.8 Case study: Stonecutters Bridge

15.5 Extreme Value of Non-Stationary Response

15.5.1 Background

15.5.2 Approximate estimation of extreme value

15.5.3 Possion approximation

15.5.4 Vanmarcke approximation

15.5.5 Statistical moment of extreme value

15.6 Unconditional Simulation of Non-Stationary Wind

15.6.1 Background

15.6.2 Unconditional simulation

15.7 Conditional Simulation of Non-Stationary Wind

15.7.1 Background

15.7.2 Problem statement

15.7.3 Conditional simulation method

15.7.4 Computational difficulties in conditional simulation

15.7.5 Fast algorithm for conditional simulation method

15.7.6 Fast algorithm for conditional simulation

15.7.7 Implementation procedure

15.7.8 Validation and application

15.8 Nonlinear Buffeting Response

15.8.1 Introduction

15.8.2 Linearization model for nonlinear aerodynamic forces

15.8.3 Hysteretic behavior of nonlinear aerodynamic forces

15.8.4 Hysteretic models for nonlinear aerodynamic forces

15.8.5 ANN-based hysteretic model of nonlinear buffeting response

15.9 References

15.10 Notations

16 Epilogue: Challenges and Prospects

16.1 Challenges

16.1.1 Typhoon wind characteristics and topography effects

16.1.2 Effects of non-stationary and non-Gaussian winds

16.1.3 Effects of aerodynamic nonlinearity

16.1.4 Wind effects on coupled vehicle-bridge systems

16.1.5 Rain-wind-induced vibration of stay cables

16.1.6 Uncertainty and reliability analysis

16.1.7Advancing computational wind engineering and wind tunnel test techniques

16.1.8 Application of wind and structural health monitoring technique

16.2 Prospects

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